Capacitively-shunted asymmetric DC-SQUID for qubit readout and reset

ABSTRACT

A tunable resonator is formed by shunting a set of asymmetric DC-SQUIDs with a capacitive device. An asymmetric DC-SQUID includes a first Josephson junction and a second Josephson junction, where the critical currents of the first and second Josephson junctions are different. A coupling is formed between the tunable resonator and a qubit such that the capacitively-shunted asymmetric DC-SQUIDs can dispersively read a quantum state of the qubit. An external magnetic flux is set to a first value and applied to the tunable resonator. A first value of the external magnetic flux causes the tunable resonator to tune to a first frequency within a first frequency difference from a resonance frequency of the qubit, the tunable resonator tuning to the first frequency causes active reset of the qubit.

TECHNICAL FIELD

The present invention relates generally to a superconducting device, afabrication method, and fabrication system for reading a superconductingqubit state and resetting the superconducting qubit to a ground state.More particularly, the present invention relates to a device, method,and system for a tunable asymmetric DC-SQUID for qubit readout andreset.

BACKGROUND

Hereinafter, a “Q” prefix in a word of phrase is indicative of areference of that word or phrase in a quantum computing context unlessexpressly distinguished where used.

Molecules and subatomic particles follow the laws of quantum mechanics,a branch of physics that explores how the physical world works at themost fundamental levels. At this level, particles behave in strangeways, taking on more than one state at the same time, and interactingwith other particles that are very far away. Quantum computing harnessesthese quantum phenomena to process information.

The computers we use today are known as classical computers (alsoreferred to herein as “conventional” computers or conventional nodes, or“CN”). A conventional computer uses a conventional processor fabricatedusing semiconductor materials and technology, a semiconductor memory,and a magnetic or solid-state storage device, in what is known as a VonNeumann architecture. Particularly, the processors in conventionalcomputers are binary processors, i.e., operating on binary datarepresented in 1 and 0.

A quantum processor (q-processor) uses the odd nature of entangled qubitdevices (compactly referred to herein as “qubit,” plural “qubits”) toperform computational tasks. In the particular realms where quantummechanics operates, particles of matter can exist in multiplestates—such as an “on” state, an “off” state, and both “on” and “off”states simultaneously. Where binary computing using semiconductorprocessors is limited to using just the on and off states (equivalent to1 and 0 in binary code), a quantum processor harnesses these quantumstates of matter to output signals that are usable in data computing.

Conventional computers encode information in bits. Each bit can take thevalue of 1 or 0. These 1s and 0s act as on/off switches that ultimatelydrive computer functions. Quantum computers, on the other hand, arebased on qubits, which operate according to two key principles ofquantum physics: superposition and entanglement. Superposition meansthat each qubit can represent both a 1 and a 0 at the same time.Entanglement means that qubits in a superposition can be correlated witheach other in a non-classical way; that is, the state of one (whether itis a 1 or a 0 or both) can depend on the state of another, and thatthere is more information that can be ascertained about the two qubitswhen they are entangled than when they are treated individually.

Using these two principles, qubits operate as more sophisticatedprocessors of information, enabling quantum computers to function inways that allow them to solve difficult problems that are intractableusing conventional computers. IBM has successfully constructed anddemonstrated the operability of a quantum processor usingsuperconducting qubits (IBM is a registered trademark of InternationalBusiness Machines corporation in the United States and in othercountries.)

A superconducting qubit includes a Josephson junction. A Josephsonjunction is formed by separating two thin-film superconducting metallayers by a non-superconducting material. When the metal in thesuperconducting layers is caused to become superconducting—e.g. byreducing the temperature of the metal to a specified cryogenictemperature—pairs of electrons can tunnel from one superconducting layerthrough the non-superconducting layer to the other superconductinglayer. In a qubit, the Josephson junction—which functions as adispersive nonlinear inductor—is electrically coupled in parallel withone or more capacitive devices forming a nonlinear microwave oscillator.The oscillator has a resonance/transition frequency determined by thevalue of the inductance and the capacitance in the qubit circuit. Anyreference to the term “qubit” is a reference to a superconducting qubitcircuitry that employs a Josephson junction, unless expresslydistinguished where used.

The information processed by qubits is carried or transmitted in theform of microwave signals/photons in the range of microwave frequencies.The microwave signals are captured, processed, and analyzed to decipherthe quantum information encoded therein. A readout circuit is a circuitcoupled with the qubit to capture, read, and measure the quantum stateof the qubit. An output of the readout circuit is information usable bya q-processor to perform computations.

A superconducting qubit has two quantum states—|0> and |1>. These twostates may be two energy states of atoms, for example, the ground (|g>)and first excited state (|e>) of a superconducting artificial atom(superconducting qubit). Other examples include spin-up and spin-down ofthe nuclear or electronic spins, two positions of a crystalline defect,and two states of a quantum dot. Since the system is of a quantumnature, any combination of the two states are allowed and valid.

For quantum computing using qubits to be reliable, quantum circuits,e.g., the qubits themselves, the readout circuitry associated with thequbits, and other parts of the quantum processor, must not alter theenergy states of the qubit, such as by injecting or dissipating energy,in any significant manner or influence the relative phase between the|0> and |1> states of the qubit. This operational constraint on anycircuit that operates with quantum information necessitates specialconsiderations in fabricating semiconductor and superconductingstructures that are used in such circuits.

A reset of a qubit is the process by which the qubit's energy statereturns from an excited state to a ground state. A time constant (T₁)characterizes the exponential decay versus time of the excited energystate of the qubit to the ground state.

In general, a superconducting quantum interference device (SQUID) isused as a very sensitive magnetometer that can measure extremely lowmagnetic fields. SQUIDs are sensitive enough to measure fields as low as5 atto Tesla (5×10⁻¹⁸ aT). For comparison, a typical refrigerator magnetproduces 0.01 tesla (10⁻² T).

There are two main types of SQUID: direct current (DC) SQUID and radiofrequency (RF) SQUID.

A dc-SQUID is based on the DC Josephson effect and has two Josephsonjunctions in parallel in a superconducting loop. In the absence of anyexternal magnetic field, the input current splits into the twobranches—one to each Josephson junction in the loop—equally. If a smallexternal magnetic field is applied to the superconducting loop, ascreening current, begins circulating in the loop that generates amagnetic field canceling the applied external flux. The induced currentis in the same direction as in one of the branches of thesuperconducting loop, and is opposite to in the other branch; the totalcurrent becomes in one branch and in the other branch. As soon as thecurrent in either branch exceeds the critical current I_(c) of theJosephson junction in that branch, a voltage appears across thatjunction. If the external flux is further increased until it exceeds,half the magnetic flux quantum, because the flux enclosed by thesuperconducting loop must be an integer number of flux quanta, insteadof screening the flux the SQUID now energetically prefers to increase itto towards a flux quantum. The screening current now flows in theopposite direction. Thus, the screening current changes direction everytime the flux increases by half integer multiples of flux quantum. Thus,the critical current oscillates in the superconducting loop of thedc-SQUID as a function of the applied flux.

The illustrative embodiments recognize that presently, a significantamount of time is wasted in waiting for the qubit to reset. Generally,for long-lived qubits the decay of the excited state to the ground stateis slow. Consequently, the reset operation that is based on waiting forthe qubit to decay to the ground state is also slow. The longer the T₁of the qubit the longer is the idle time.

The illustrative embodiments recognize that this wastage of time has adirect adverse effect on the speed of quantum computations that arepossible using superconducting qubits. The illustrative embodimentsfurther recognize that because the commonly used method for reset ispassive, i.e., not performed using circuit other than the qubit itself,other quantum circuits, such as the readout circuit that is presentlyemployed for reading qubits, play no role in resetting the qubit.

The illustrative embodiments recognize that an active method ofresetting the qubit is therefore desirable. In the active method, aquantum circuit external to the qubit operates in a manner to force thequbit to the ground energy state, accelerates the decay of the qubit tothe ground energy state, or some combination thereof. The illustrativeembodiments further recognize that a quantum circuit that is capable ofmultiple operations, such as both readout and reset operations on aqubit, is also highly desirable.

SUMMARY

The illustrative embodiments provide a superconducting device, and amethod and system of fabrication therefor. A superconducting device ofan embodiment includes a capacitive device shunting a set of asymmetricDC-SQUIDs to form a tunable resonator, an asymmetric DC-SQUID in the setof asymmetric DC-SQUIDs comprising a first Josephson junction and asecond Josephson junction, wherein a first critical current of the firstJosephson junction is different from a second critical current of thesecond Josephson junction. The superconducting device includes acoupling between the tunable resonator and a qubit such that thecapacitively-shunted asymmetric DC-SQUIDs can dispersively read aquantum state of the qubit. An external magnetic flux is set to a firstvalue and applied to the tunable resonator, wherein a first value of theexternal magnetic flux causes the tunable resonator to tune to a firstfrequency, wherein the first frequency is within a first frequencydifference from a resonance frequency of the qubit, and wherein thetunable resonator tuning to the first frequency causes active reset ofthe qubit. Thus, the embodiment provides a superconducting device thatis capable of performing an active reset of a qubit.

In another embodiment, the external magnetic flux is changed to a secondvalue, wherein the second value of the external magnetic flux causes thetunable SQUID to tune to a second frequency, wherein the secondfrequency is detuned from the resonance frequency of the qubit by atleast a second frequency difference, and wherein the tunable resonatortuning to the second frequency enables dispersive readout operation ofthe quantum state of the qubit to be performed by sending a microwavesignal to the qubit-resonator system at the resonance frequency of theresonator and measuring the amplitude and/or the phase of the outputsignal. Thus, the embodiment provides a superconducting device that iscapable of performing a readout as well as an active reset of a qubit.

In another embodiment, the second frequency is a maximum frequency in afrequency resonance range of the tunable resonator. Thus, the embodimentprovides a particular manner of operating the superconducting device forperforming the readout.

In another embodiment, the second frequency difference is a function ofa degree of asymmetry between the first Josephson junction and thesecond Josephson junction. Thus, the embodiment provides a particularmanner of configuring the superconducting device for performing thereadout.

In another embodiment, the first frequency distance is zero and thefirst frequency is the resonance frequency of the qubit. Thus, theembodiment provides a particular manner of operating the superconductingdevice for performing the active reset.

In another embodiment, the first frequency being within the firstfrequency difference from the resonance frequency of the qubit causesthe qubit to release a photon, the releasing causing the qubit to relaxto a ground energy state. Thus, the embodiment provides a particularmechanism by which the superconducting device performs the reset.

In another embodiment, forcing the qubit to the ground energy state isfaster than an energy decay time constant of the qubit. Thus, theembodiment provides a particular mechanism by which the reset performedby the superconducting device is an active reset.

In another embodiment, the set of asymmetric DC-SQUIDs includes only theasymmetric DC-SQUID. Thus, the embodiment provides a superconductingdevice in one alternative configuration.

Another embodiment further includes a series connection connecting aplurality of asymmetric DC-SQUIDs from the set of asymmetric DC-SQUIDs.Thus, the embodiment provides a superconducting device in anotheralternative configuration.

In another embodiment, the series connection comprises a superconductingwire. Thus, the embodiment provides a particular configuration in onealternative configuration of the superconducting device.

Another embodiment further includes a first pad formed on a first sideof the set of asymmetric DC-SQUIDs. The embodiment includes a second padforming on a second side of the set of asymmetric DC-SQUIDs, wherein thefirst pad and the second pad are separated by a distance, and whereinthe first pad and the second pad together form the capacitive device.Thus, the embodiment provides another particular configuration in onealternative configuration of the superconducting device.

An embodiment includes a fabrication method for fabricating thesuperconducting device.

An embodiment includes a fabrication system for fabricating thesuperconducting device.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features believed characteristic of the invention are setforth in the appended claims. The invention itself, however, as well asa preferred mode of use, further objectives and advantages thereof, willbest be understood by reference to the following detailed description ofthe illustrative embodiments when read in conjunction with theaccompanying drawings, wherein:

FIG. 1 depicts some example configurations of a capacitively-shuntedasymmetric DC-SQUID in accordance with an illustrative embodiment;

FIG. 2 depicts a circuit schematic of a tunable asymmetric DC-SQUID forqubit readout and reset used in accordance with an illustrativeembodiment;

FIG. 3 depicts two example realizations of tunable resonators aredepicted in accordance with an illustrative embodiment;

FIG. 4 depicts one example configuration of a tunable resonator foractive reset and readout of a qubit in accordance with an illustrativeembodiment;

FIG. 5 depicts another example configuration of a tunable resonator foractive reset and readout of a different qubit in accordance with anillustrative embodiment; and

FIG. 6 depicts another example configuration of a tunable resonator foractive reset and readout of a superconducting qubit in accordance withan illustrative embodiment.

DETAILED DESCRIPTION

The illustrative embodiments used to describe the invention generallyaddress and solve the above-described needs for a tunablesuperconducting resonator for qubit readout and reset. The tunableresonator can be realized as a capacitively-shunted asymmetric DC-SQUIDarray.

An embodiment can be implemented as a capacitively-shunted asymmetricDC-SQUID. A design and fabrication method for the capacitively-shuntedasymmetric SQUID can be implemented as a software application. Theapplication implementing an embodiment can be configured to operate inconjunction with an existing superconductor fabrication system—such as alithography system.

For the clarity of the description, and without implying any limitationthereto, the illustrative embodiments are described using some examplenumbers of SQUIDs. An embodiment can be implemented with a differentnumber of SQUIDs within the scope of the illustrative embodiments.

Furthermore, simplified diagrams of the example SQUIDs, qubits, andother circuit components are used in the figures and the illustrativeembodiments. In an actual fabrication or circuit, additional structuresor component that are not shown or described herein, or structures orcomponents different from those shown and described herein, may bepresent without departing the scope of the illustrative embodiments.Similarly, within the scope of the illustrative embodiments, a shown ordescribed component in the example capacitively-shunted asymmetricDC-SQUID may be fabricated or coupled differently to yield a similaroperation or result as described herein.

A specific value, location, position, or dimension of a component ofcapacitively-shunted asymmetric DC-SQUID described herein is notintended to be limiting on the illustrative embodiments unless such acharacteristic is expressly described as a feature of an embodiment. Thevalue, location, position, dimension, or some combination thereof, arechosen only for the clarity of the drawings and the description and mayhave been exaggerated, minimized, or otherwise changed from actualvalue, location, position, or dimension that might be used in actualfabrication or circuit to achieve an objective according to theillustrative embodiments.

Furthermore, the illustrative embodiments are described with respect tospecific actual or hypothetical components only as examples. The stepsdescribed by the various illustrative embodiments can be adapted forfabricating a circuit using a variety of similarly purposed componentsin a similar manner, and such adaptations are contemplated within thescope of the illustrative embodiments.

The illustrative embodiments are described with respect to certain typesof materials, electrical properties, structures, formations, steps,operations, dimensions, numerosity, frequencies, circuits, components,and applications only as examples. Any specific manifestations of theseand other similar artifacts are not intended to be limiting to theinvention. Any suitable manifestation of these and other similarartifacts can be selected within the scope of the illustrativeembodiments.

The examples in this disclosure are used only for the clarity of thedescription and are not limiting to the illustrative embodiments. Anyadvantages listed herein are only examples and are not intended to belimiting to the illustrative embodiments. Additional or differentadvantages may be realized by specific illustrative embodiments.Furthermore, a particular illustrative embodiment may have some, all, ornone of the advantages listed above.

With reference to FIG. 1, this figure depicts some exampleconfigurations of a capacitively-shunted asymmetric DC-SQUID inaccordance with an illustrative embodiment. Configuration 100 forms oneexample configuration of a capacitively-shunted asymmetric DC-SQUID inwhich a single (N=1) asymmetric dc-SQUID 102 is used.

Josephson junction 102-1 and Josephson junction 102-2 are shown in theirrespective positions only as non-limiting examples. The positions of theJosephson junctions can be interchanged with one another in thesuperconducting loop of SQUID 102 assuming that input current I isdelivered via a wire that is centered between Josephson junctions 102-1and 102-2.

Asymmetric dc-SQUID 102 is a modification of a symmetric dc-SQUID inthat the two Josephson junctions 102-1 and 102-2 in SQUID 102 havedifferent critical currents (generally have different areas), asrepresented by the different sizes (not to scale) of the symbols (cross)representing the Josephson junctions in SQUID 102. Josephson junction102-1 has critical current I_(c1). Josephson junction 102-2 has criticalcurrent I_(c2). According to the illustrative embodiments, Josephsonjunctions 102-1 and 102-2 are desirably of different sizes so as toallow when shunted by a capacitance for a limited band of tunablefrequencies (frequency resonance range) of the device 100 or 150. Forexample, if the frequency of the qubit (not shown) that is to be read orreset is in the neighborhood of 4.7 Gigahertz (GHz), a desirable limitedband of tunable frequency might range from 4.5 GHz to 8.5 GHz. If thesizes of the two Josephson junctions in SQUID 102 were identical, ornear-identical, the bottom of the frequency range of thecapacitively-shunted SQUID would approach vanishing frequencies,assuming the high limit of the range remained unchanged. As one ofordinary skill in the art would appreciate, a larger frequency bandleads to steeper slopes between the peaks and troughs of the frequencytunability graph. The significance of ending the frequency range justbelow the frequency of the qubit, and the resulting smaller slopes inthe frequency tunability curve of the capacitively-shunted SQUID, willbecome clearer from FIGS. 4-6 described herein. Asymmetric Josephsonjunctions 102-1 and 102-2, when selected suitably, allow a stablefrequency minimum of the frequency range of the capacitively-shuntedasymmetric DC-SQUID 102.

Asymmetric DC-SQUID 102 is shunted (electrically coupled in parallel)with capacitive device 104. Capacitor 104 in parallel with theinductance of asymmetric DC-SQUID 102 forms capacitively-shuntedasymmetric DC-SQUID 100 which functions as a tunable resonator. Tunableresonator 100 operates as a resonator whose frequency is tunable orchangeable by tuning or adjusting an external magnetic flux (Φ_(ext))applied to tunable SQUID 100. It is assumed that the inductance of thesuperconducting loops of the SQUIDs 102 is small and satisfies theinequality L(I_(c1)+I_(c2))<<Φ_(ext). This assumption mainly simplifiesthe analysis and the calculation of the device response, because itimplies that the total flux threading the dc-SQUID loop is equal oralmost equal to the applied external flux Φ_(ext).

Tunable resonator 100 can be coupled with a qubit (not shown) and/or aninput/output transmission line (not shown) of a circuit (not shown)using nodes 106 and 108. By adjusting the external flux, tunableresonator 100 exhibits a resonance frequency response which lies withinthe frequency range, which is set at least in part by the chosenasymmetrical critical currents (sizes) of Josephson junctions 102-1 and102-2, and the size of capacitor 104. This tunable frequency of thetunable resonator 100 can be tuned to be the same as or close to thetransition frequency of the qubit (qubit resonance frequency), or can betuned to be at the far end of the frequency range from the frequency ofthe qubit. When the frequency of tunable resonator 100 is tuned to bethe same as or close to the frequency of the qubit, tunable resonator100—which in principle is a resonator—is said to be in resonance withthe qubit. When the frequency of tunable resonator 100 is tuned to besignificantly different from the frequency of the qubit, tunableresonator 100 is said to be out of resonance with the qubit.

Tunable SQUID-based resonator 100 can thus be tuned to actively reset orread the qubit by simply tuning the inductance of SQUID 102, this inturn tunes the resonator in or out of resonance with the qubit. When thequbit state is to be reset/initialized into the ground state, thefrequency of tunable resonator 100 is tuned into resonance with thequbit resonance frequency. This in-resonance tuning of tunable resonator100 stimulates emission of a photon from the qubit into the readoutresonator (tunable resonator 100) through the Purcell effect andconsequently leaves the qubit in the ground state.

When the qubit state is to be read out or otherwise manipulated, thefrequency of the readout resonator (tunable resonator 100) is tuned outof resonance with the qubit resonance frequency. In this mode ofoperation, the qubit state is read using the dispersive readouttechnique. In this case, the tunable resonator frequency is parked at asweet spot corresponding to the maximum resonance frequency of thereadout resonator versus flux. The sweet spot has a zero slope (or nearzero slope) region of the frequency tunability curve of tunableresonator 100 versus flux. The zero-slope point or the near-zero sloperegion minimizes the susceptibility of the readout resonator frequencyto flux noise.

Configuration 150 forms another example configuration of a tunableresonator in which a plurality (N>1) of asymmetric dc-SQUIDs 152A, 152B. . . 152N are used. Each of asymmetric DC-SQUIDs 152A-N is configuredand operates in the manner of asymmetric DC-SQUID 102 in tunableresonator 100.

Asymmetric DC-SQUIDs 152A-N are linked in series as shown. The series ofasymmetric DC-SQUIDs 152A-N is shunted with capacitor 154. Capacitor 154is similar in function to capacitor 104 in tunable resonator 100, butmay be different in size according to the inductance of asymmetricDC-SQUID series 152 and the frequency resonance range desired fromtunable SQUID 152. Nodes 156 and 158 correspond to nodes 106 and 108,respectively, in tunable resonator 100.

In one embodiment, each asymmetric DC-SQUID 152A, 152B, 152N issubstantially identical to one another. In another embodiment, series152 can include an asymmetric DC-SQUID that has the same or differentsizes of one or both Josephson junctions as compared to anotherasymmetric DC-SQUID in the series.

With reference to FIG. 2, this figure depicts a circuit schematic of atunable asymmetric DC-SQUID for qubit readout and reset used inaccordance with an illustrative embodiment. Resonator 202 can be tunableSQUID 100 or tunable SQUID 150 from FIG. 1. In the depicted non-limitingexample, resonator 202 is tunable SQUID 150.

Resonator 202 is configured to read and reset qubit 204. Qubit 204 isformed using Josephson junction 206 and capacitor 208. Josephsonjunction 206 has a critical current of I_(cq) and capacitor 208 has acapacitance of C_(q). Node 156 (or 106 as the case may be) couples withqubit 204 via coupling capacitor 210 of capacitance C_(c). Node 156 (or106 as the case may be) couples with input/output transmission line 212via readout capacitor 214 of capacitance C_(r). Node 158 (or 108 as thecase may be) couples with qubit 204 as shown.

With reference to FIG. 3, two example realizations of tunable resonatorsare depicted in accordance with an illustrative embodiment. Tunableresonator 300 is substantially similar in functionality to tunableresonator 100 of FIG. 1. Tunable resonator 350 is substantially similarin functionality to tunable resonator 150 of FIG. 1.

Capacitor 104 in tunable SQUID can be fabricated in a variety ofimplementation-specific ways, using a variety of lithography methods. Inone such method, pads 304A and 304B are formed and coupled with tunableSQUID 102 via nodes 106 and 108 respectively, as shown. Pads 304A and304B, fabricated of a superconducting material, are separated by adistance/gap d1, thereby forming a capacitor, i.e., capacitor 104 oftunable resonator 100. In one embodiment, pads 304A and 304B areco-planar, i.e., in the same plane of fabrication.

Capacitor 154 can be similarly fabricated for tunable SQUID 154. Forexample, pads 354A and 354B, fabricated of a superconducting material,are separated by a distance d2, thereby forming a capacitor, i.e.,capacitor 154 of tunable SQUID 100. In one embodiment, pads 354A and354B are co-planar.

With reference to FIG. 4, this figure depicts one example configurationof a tunable resonator for active reset and readout of a qubit inaccordance with an illustrative embodiment. Only as a non-limitingexample, in one configured experiment, tunable resonator 402 wasconfigured in the manner of tunable resonator 350 of FIG. 3, with eight(N=8) similar asymmetric DC-SQUIDs in series 404. For each asymmetricDC-SQUID in series 404, I_(c1) was 400 nanoamperes (nA) and I_(c2) was800 nA. Capacitance C between pads 306A and 306B—which operate as theshunt capacitor in tunable resonator 402—was 175 femto-Farad (fF). Theseries inductance of series 404 was 0.1 nanoHenry (nH). Tunableresonator 402 was configured to readout and reset a qubit (not shown)whose resonance frequency f_(q) was 4.73 GHz.

Graph 408 plots the change in the resonance frequency of tunableresonator 402 when Φ_(ext) changes, where Φ_(ext) is the appliedexternal flux threading the loop of each dc-SQUID. The X-axis of graph408 represents the ratio Φ_(ext)/φ₀, where Φ₀ is flux quantum. TheY-axis of graph 408 plots the resonance frequency of the device as afunction of the ratio Φ_(ext)/Φ₀.

As graph 408 shows, resonance frequency peaks with zero slopes occurwhen Φ_(ext) is an integer multiple of Φ₀. Resonance frequency valleyswith zero slopes occur when Φ_(ext) is a plus or minus odd-integermultiple of Φ₀/2. Tunable resonator 402 is constructed with suitableasymmetric Josephson junctions and capacitance C such that the resonancefrequency valley with zero slope points occur at or near f_(q).

When tunable resonator 402 is tuned to a resonance frequency peak withzero slope (detuned far from qubit frequency), by varying Φ_(ext), e.g.,point 410 or another zero-slope resonance frequency peak point (amaximum frequency), the qubit can be read out as described herein. Inthe calculation example, which uses the depicted configuration, azero-slope resonance frequency peak was reached at 8.071 GHz.

When tunable resonator 402 is tuned to a resonance frequency valley withzero slope by varying text, e.g., point 412 or another zero-sloperesonance frequency valley point (a minimum frequency), the qubit can bereset as described herein. In the calculation example, which uses thedepicted configuration, a zero-slope resonance frequency valley wasreached at 4.73 GHz.

With reference to FIG. 5, this figure depicts another exampleconfiguration of a tunable resonator for active reset and readout of adifferent qubit in accordance with an illustrative embodiment. Tunableresonator 502 was configured substantially in the manner described withrespect to FIG. 4, but with series inductance L=0.8 nH. Series 504 isconfigured substantially in the manner of series 404 but with thedifferent series inductance, e.g., by changing the shape, size, ormaterial of the superconducting wires. Pads 506A and 506B form the shuntcapacitor substantially in the manner of pads 406A and 406B.

Tunable resonator 502 was configured to readout and reset a qubit (notshown) whose resonance frequency f_(q) was 4.5 GHz. Graph 508 plots thechange in the resonance frequency of tunable resonator 502 as a functionof Φ_(ext), in the manner of graph 408.

When tunable SQUID 502 is tuned to a zero slope peak point (detuned farfrom qubit frequency), by varying Φ_(ext), e.g., point 510 or anotherzero slope peak point, the qubit can be readout as described herein. Inthe calculation example, which uses the depicted configuration, azero-slope resonance frequency peak was reached at 7.038 GHz.

When tunable SQUID 502 is tuned to a zero-slope resonance frequencyvalley (minimum) by varying Φ_(ext), e.g., point 512 or anotherzero-slope resonance frequency valley point, the qubit can be reset asdescribed herein. In the calculation example, which uses the depictedconfiguration, a zero-slope resonance frequency valley was reached at4.5 GHz.

With reference to FIG. 6, this figure depicts another exampleconfiguration of a tunable resonator for active reset and readout of asuperconducting qubit in accordance with an illustrative embodiment.Only as a non-limiting example, in one configured experiment, tunableresonator 602 was configured in the manner of tunable resonator 300 ofFIG. 3, with a single (N=1) asymmetric DC-SQUID 604. When constructing atunable resonator with a single asymmetric DC-SQUID, as in this case, arisk of possible hybridization effects between the energy states of thequbit and the qubit-like resonator exists. Such a configuration shouldbe theoretically analyzed in order to verify there is no undesiredeffects.

For asymmetric DC-SQUID 604, I_(c1) was 40 nA and I_(c2) was 80 nA.Capacitance C between pads 606A and 606B—which operate as the shuntcapacitor in tunable resonator 300—was 175 fF. The series inductanceasymmetric DC-SQUID 604 was 0.1 nH. Tunable resonator 602 was configuredto readout and reset a qubit (not shown) whose resonance frequency f_(q)was 4.2 GHz.

Graph 608 plots the change in the resonance frequency of tunableresonator 602 when Φ_(ext) is varied, in the manner of graph 408 or 508.

When tunable resonator 602 is tuned to a zero-slope resonance frequencypeak (detuned far from qubit frequency), by varying Φ_(ext), e.g., point610 or another zero-slope resonance frequency peak, the qubit can bereadout as described herein. In the calculation example, which uses thedepicted configuration, a zero-slope resonance frequency peak wasreached at 7.251 GHz.

When tunable resonator 602 is tuned to a zero-slope resonance frequencyvalley point by varying text, e.g., point 612 or another zero-sloperesonance frequency valley point, the qubit can be reset as describedherein. In the calculation example, which uses the depictedconfiguration, a zero-slope resonance frequency valley was reached at4.2 GHz.

A tunable resonator in the form of a capacitively shunted asymmetricDC-SQUID according to an embodiment described herein is compact in sizeand has a small footprint, can be fabricated using the same fabricationprocess as the qubits, provides a mechanism for fast qubit reset, has ahigh internal Q (>2 M), has a low participation ratio on surfaces, andhas high Q Josephson junctions (higher Q than superconductingmeander-line inductors). Furthermore, the capacitively shuntedasymmetric DC-SQUID according to an embodiment eliminates the need for afast readout resonator to reset qubits, as that apparatus is known toshorten the qubit lifetime T₁. Additionally, using a capacitivelyshunted asymmetric DC-SQUID according to an embodiment to perform reset(by tuning it in resonance with the qubit), there is no need for qubitmeasurement and feedback to reset the qubit state.

What is claimed is:
 1. A superconducting device comprising: a capacitive device shunting a set of asymmetric DC-SQUIDs to form a tunable resonator, an asymmetric DC-SQUID in the set of asymmetric DC-SQUIDs comprising a first Josephson junction and a second Josephson junction, wherein a first critical current of the first Josephson junction is different from a second critical current of the second Josephson junction; a coupling between the tunable resonator and a qubit such that the capacitively-shunted asymmetric DC-SQUIDs can read a quantum state of the qubit; and an external magnetic flux, wherein the external magnetic flux is set to a first value and applied to the tunable resonator, wherein a first value of the external magnetic flux causes the tunable resonator to tune to a first frequency, and wherein the tunable resonator tuning to the first frequency causes active reset of the qubit.
 2. The superconducting device of claim 1, further comprising: the external magnetic flux changed to a second value, wherein the second value of the external magnetic flux causes the tunable SQUID to tune to a second frequency, wherein the first frequency is within a first frequency difference from a resonance frequency of the qubit, wherein the second frequency is detuned from the resonance frequency of the qubit by at least a second frequency difference, and wherein the tunable resonator tuning to the second frequency enables a dispersive readout operation of the quantum state of the qubit to be performed.
 3. The superconducting device of claim 2, wherein the second frequency is a maximum frequency in a frequency resonance range of the tunable resonator.
 4. The superconducting device of claim 2, wherein the second frequency difference is a function of a degree of asymmetry between the first Josephson junction and the second Josephson junction.
 5. The superconducting device of claim 1, wherein the first frequency difference is zero and the first frequency is the resonance frequency of the qubit.
 6. The superconducting device of claim 1, wherein the first frequency being within the first frequency difference from the resonance frequency of the qubit causes the qubit to release a photon, the releasing causing the qubit to relax to a ground energy state.
 7. The superconducting device of claim 6, wherein forcing the qubit to the ground energy state is faster than an energy decay time constant of the qubit.
 8. The superconducting device of claim 1, wherein the set of asymmetric DC-SQUIDs includes only the asymmetric DC-SQUID.
 9. The superconducting device of claim 1, further comprising: a series connection connecting a plurality of asymmetric DC-SQUIDs from the set of asymmetric DC-SQUIDs.
 10. The superconducting device of claim 9, wherein the series connection comprises a superconducting wire.
 11. The superconducting device of claim 1, further comprising: a first pad formed on a first side of the set of asymmetric DC-SQUIDs; and a second pad forming on a second side of the set of asymmetric DC-SQUIDs, wherein the first pad and the second pad are separated by a distance, and wherein the first pad and the second pad together form the capacitive device.
 12. A method comprising: forming a tunable resonator by shunting a set of asymmetric DC-SQUIDs with a capacitive device, an asymmetric DC-SQUID in the set of asymmetric DC-SQUIDs comprising a first Josephson junction and a second Josephson junction, wherein a first critical current of the first Josephson junction is different from a second critical current of the second Josephson junction; coupling the tunable resonator to a qubit such that the tunable resonator can dispersively read a quantum state of the qubit; and actively resetting the qubit by applying an external magnetic flux of a first value to the tunable resonator, wherein a first value of the external magnetic flux causes the tunable resonator to tune to a first frequency, wherein the first frequency is within a first frequency difference from a resonance frequency of the qubit.
 13. The method of claim 12, further comprising: changing the external magnetic flux to a second value, wherein the second value of the external magnetic flux causes the tunable resonator to tune to a second frequency, wherein the second frequency is detuned from the resonance frequency of the qubit by at least a second frequency difference; and performing, using the tunable resonator tuned to the second frequency, a dispersive readout operation of the quantum state of the qubit.
 14. The method of claim 13, wherein the second frequency is a maximum frequency in a frequency resonance range of the tunable resonator.
 15. The method of claim 13, wherein the second frequency difference is a function of a degree of asymmetry between the first Josephson junction and the second Josephson junction.
 16. The method of claim 12, wherein the first frequency difference is zero and the first frequency is the resonance frequency of the qubit.
 17. The method of claim 12, wherein the first frequency being within the first frequency difference from the resonance frequency of the qubit causes the qubit to release a photon, the releasing causing the qubit to relax to a ground state.
 18. The method of claim 17, wherein forcing the qubit to the ground energy state is faster than an energy decay time constant T₁ of the qubit.
 19. The method of claim 12, wherein the set of asymmetric DC-SQUIDs includes only the asymmetric DC-SQUID.
 20. The method of claim 12, further comprising: connecting a plurality of asymmetric DC-SQUIDs from the set of asymmetric DC-SQUIDs in a series.
 21. The method of claim 20, wherein the plurality of asymmetric DC-SQUIDs is connected in series using a superconductor.
 22. The method of claim 12, further comprising: forming a first pad on a first side of the set of asymmetric DC-SQUIDs; and forming a second pad on a second side of the set of asymmetric DC-SQUIDs, wherein the first pad and the second pad are separated by a distance, and wherein the first pad and the second pad together form the capacitive device.
 23. A superconducting fabrication system which when operated to fabricate a tunable resonator device performing operations comprising: forming the tunable resonator by shunting a set of asymmetric DC-SQUIDs with a capacitive device, an asymmetric DC-SQUID in the set of asymmetric DC-SQUIDs comprising a first Josephson junction and a second Josephson junction, wherein a first critical current of the first Josephson junction is different from a second critical current of the second Josephson junction; coupling the tunable resonator to a qubit such that the tunable resonator can dispersively read a quantum state of the qubit; and actively resetting the qubit by applying an external magnetic flux of a first value to the tunable resonator, wherein a first value of the external magnetic flux causes the tunable resonator to tune to a first frequency, wherein the first frequency is within a first frequency difference from a resonance frequency of the qubit.
 24. The superconducting fabrication system of claim 23, further comprising: changing the external magnetic flux to a second value, wherein the second value of the external magnetic flux causes the tunable resonator to tune to a second frequency, wherein the second frequency is detuned from the resonance frequency of the qubit by at least a second frequency difference; and performing, using the tunable resonator tuned to the second frequency, a dispersive readout operation of the quantum state of the qubit.
 25. The superconducting fabrication system of claim 24, wherein the second frequency is a maximum frequency in a frequency resonance range of the tunable resonator. 